Blender supported 3D files that support armature
Two possibilities depending on the tools used:


Use OBJ files in combination with BVH. BVH contains the skeleton,
and OBJ is capable of containing vertex weights
DAE which is one file that can contain both the weights and the
    skeleton. This is the best format IMO and is widely supported
    (although perhaps slightly less supported than OBJ/BHV).


If FBX is your only option, I've used a program that converts FBX to DAE.

http://usa.autodesk.com/adsk/servlet/pc/item?siteID=123112&amp;id=20481519